When a ship arrives at a harbor, it is docking at one of six berths. If all six berths are occupied, the ship leaves the harbor immediately. After docking at a berth, the ship waits for the unloading service of a single crane. The crane unloads the ships in a First-In-First-Out discipline. After unloading, the ship leaves the harbor immediately. Define the system state at time t as [U(t),C(t)], where U(t)= number of ships waiting to be unloaded or being unloaded C(t)= number of busy cranes ( 0 or 1 ) Let [u,c] be the current state of the system. Define events and write the corresponding state transitions

The given problem describes a docking system of ships at a harbor. When a ship arrives at the harbor, it docks at one of six berths. If all six berths are occupied, the ship leaves the harbor immediately. After docking, the ship waits for the unloading service of a single crane. The crane unloads the ships in a First-In-First-Out discipline.

After unloading, the ship leaves the harbor immediately. The system state at time t is defined as [U(t),C(t)] where U(t) represents the number of ships waiting to be unloaded or being unloaded and C(t) represents the number of busy cranes (0 or 1). Let [u, c] be the current state of the system.

Now, the state transitions can be defined as follows:

Events:
1. A ship arrives at the harbor and all berths are occupied
2. A ship arrives at the harbor and some berths are empty
3. A crane becomes available
4. A ship finishes unloading and leaves the harbor

State transitions:
1. If [u, c] = [6, 1], the ship leaves the harbor immediately. The system state remains [6, 1].
2. If [u, c] = [6, 0], the ship leaves the harbor immediately. The system state remains [6, 0].
3. If [u, c] = [0, 0], the system state becomes [0, 1].
4. If [u, c] = [n, 0] (where n is less than 6), the system state becomes [n+1, 0].
5. If [u, c] = [n, 1] (where n is less than 6), the system state becomes [n, 1].
6. If [u, c] = [1, 1], the system state becomes [0, 1].
7. If [u, c] = [n, 1] (where n is greater than 1), the system state becomes [n-1, 1].
8. If [u, c] = [0, 1], the system state remains [0, 1].

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